Long-standing problem: The nuclear level density angular-momentum dependence and isomeric data assessment

Recent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>Tc</a:mi> <a:mprescripts/> <a:none/> <a:mrow> <a:mn>91</a:mn> <a:mo>,</a:mo> <a:mn>92</a:mn> <a:mo>,</a:mo> <a:mn>93</a:mn> </a:mrow> </a:mmultiscripts> </a:math> activation for deuterons incident on <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Mo</b:mi> <b:mprescripts/> <b:none/> <b:mtext>nat</b:mtext> </b:mmultiscripts> </b:math> has become a challenge for the nuclear level density (NLD) angular-momentum dependence. Actually, replacement of the moment of inertia rigid-body value <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>I</c:mi> <c:mi>r</c:mi> </c:msub> </c:math> by half of it, within a given NLD parameter set, demands a change of the rest of NLD parameters significantly beyond their fitted limits. The corresponding uncertainty of calculated cross sections versus the NLD parameter accuracy is also higher, while use of either the same or distinct compound-nucleus and preequilibrium emission spin distributions becomes significant at higher incident energies. Nevertheless, the current way to describe experimental isomeric cross sections by using at most half of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>I</d:mi> <d:mi>r</d:mi> </d:msub> </d:math> values provides agreement of the measured and calculated data at the price of less and less correct NLDs. The moment of inertia relevance for the NLD correctness also emphasizes the value of a direct method to endorse it. Further measurements of average resonance spacings of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>s</e:mi> </e:math> -wave neutrons and protons, corresponding to different spins of the same nucleus, are therefore highly demanded.